Simple arithmetic methods (no derivatives, no decimals, no cartesian system) for solving roots that also include the most advanced algorithms (Newton, Halley, Bernoulli)of analytic geometry and infinitesimal analysis. For Morin's more recent numerical methods, see https://sites.google.com/site/arithmonic/. Also, traditional continued fractions as special cases of a new general concept, "Generalized Continued fractions" (Fractal Fractions), and the New Arithmonic Mean. From the introduction to the book La Quinta Operación Matemá - Revolución del Número, published in Venezuela.